Application of Interpolation Inequalities to the Study of Operators with Linear Fractional Endpoint Singularities in Weighted Hölder Spaces

Oleksandr Karelin, Anna Tarasenko

Institute of Basic Sciences and Engineering, Hidalgo State University, Pachuca, Mexico.

DOI: 10.4236/am.2014.517266                

Abstract

In this paper we consider operators with endpoint singularities generated by linear fractional Carleman shift in weighted Hölder spaces. Such operators play an important role in the study of algebras generated by the operators of singular integration and multiplication by function. For the considered operators, we obtained more precise relations between norms of integral operators with local singularities in weighted Lebesgue spaces and norms in weighted Hölder spaces, making use of previously obtained general results. We prove the boundedness of operators with linear fractional singularities.

Keywords

Endpoint Singularities, Weighted Holder Space, Weighted Lebesgue Spaces, Relation between Norms, Boundedness

Conflicts of Interest

The authors declare no conflicts of interest.

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